"low-quality," c. 1200, "shared by all," from imene, from Old English gemæne "common, public, general, universal, shared by all," from Proto-Germanic *ga-mainiz "possessed jointly" (source also of Old Frisian mene, Old Saxon gimeni, Middle Low German gemeine, Middle Dutch gemene, Dutch gemeen, German gemein, Gothic gamains "common"), from PIE *ko-moin-i- "held in common," a compound adjective formed from collective prefix *ko- "together" (Proto-Germanic *ga-) + *moi-n-, suffixed form of PIE root *mei- (1) "to change; exchange." Compare second element in common (adj.), a word with a sense evolution parallel to that of this word.
Of things, "inferior, second-rate," from late 14c. (a secondary sense in Old English was "false, wicked"). Notion of "so-so, mediocre" led to confusion with mean (n.). Meaning "inferior in rank or status" (of persons) emerged early 14c.; that of "ordinary" from late 14c.; that of "stingy, nasty" first recorded 1660s; weaker sense of "disobliging, pettily offensive" is from 1839, originally American English slang. Inverted sense of "remarkably good" (i.e. plays a mean saxophone) first recorded c. 1900, perhaps from phrase no mean _______ "not inferior" (1590s, also, "not average," reflecting further confusion with mean (n.)).
"occupying a middle or intermediate place," mid-14c., from Anglo-French meines (plural), Old French meien, variant of moiien "mid-, medium, common, middle-class" (12c., Modern French moyen), from Late Latin medianus "of the middle," from Latin medius "in the middle" (from PIE root *medhyo- "middle"). Meaning "intermediate in time" is from mid-15c. Mathematical sense is from late 14c.
"that which is halfway between extremes," early 14c., from Old French meien "middle, means, intermediary," noun use of adjective from Latin medianus "of or that is in the middle" (see mean (adj.2)). Oldest sense is musical; mathematical sense is from c. 1500. Some senses reflect confusion with mean (adj.1). This is the mean in by no means (late 15c.).
"intend, have in mind," Old English mænan "to mean, intend, signify; tell, say; complain, lament," from West Germanic *mainijan (source also of Old Frisian mena "to signify," Old Saxon menian "to intend, signify, make known," Dutch menen, German meinen "think, suppose, be of the opinion"), from PIE *meino- "opinion, intent" (source also of Old Church Slavonic meniti "to think, have an opinion," Old Irish mian "wish, desire," Welsh mwyn "enjoyment"), perhaps from root *men- (1) "to think." Conversational question you know what I mean? attested by 1834.
"calculate an arithmetical mean," 1882, from mean (n.).
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